Washington -LRB- CNN -RRB- -- The glitch-plagued rollout of President Barack Obama 's signature health care law has been dogged by one big question : How many people have enrolled in an insurance plan ?

The White House refuses to release the numbers , leading many to assume they are embarrassingly low . But insurance industry insiders point to another reason : Nobody knows if the numbers they do have are even accurate .

Turns out , some insurance companies say they are receiving data from the administration that is incomplete , duplicative or contradictory , making it difficult to get an accurate count of new enrollment .

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So far , most of the attention has focused on people being unable to sign up for coverage through online health care exchanges . But even when customers manage to make it through the enrollment process , glitches persist .

`` The administration is not wrong in saying that there 's been a lot of problems with signing up . But it 's incorrect to say that 's the only problem , '' an insurance industry official said . `` That 's not the only issue at hand . ''

Industry officials who were contacted requested anonymity to speak candidly because of the superheated politics surrounding Obamacare .

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The sign-up process works this way : A person sets up an online account , verifies an identity , applies for coverage and subsidies and , if eligible , shops and enrolls for a plan . Once completed , information is sent to the insurance plans selected by the user .

At 6 p.m. each day , the government sends the latest batch of new enrollees to insurance companies . But sometimes that data come with conflicting information , showing for instance , someone who enrolled and then canceled a plan , said an insurance industry executive . Other times data come in without a time stamp , making it difficult to track , the executive said .

Adding to the confusion , the executive said , is that people are not officially enrolled in a plan until they pay their first premiums , which are not due until December 15 . That means shoppers have about two months to cancel or switch plans before making a final decision of whether or not to enroll .

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An administration official did not dispute there have been problems with data sent by the government to insurers .

`` We know that people are enrolling in coverage and the system works . As individual problems are raised by insurers , we work aggressively to address them , '' said Joanne Peters , a spokeswoman for the Department of Health and Human Services .

An HHS official said enrollment numbers will likely be released in mid-November , giving officials time to verify their accuracy .

Former Obama press secretary Robert Gibbs had harsh words for the administration , saying the October 1 rollout was `` bungled badly . ''

`` I hope they 're working day and night to get this done , and when they get it fixed , I hope they fire some people that were in charge of making sure this thing was supposed to work , '' Gibbs said Monday on MSNBC .

` Cumbersome , glitchy ' system

So far , the buzz in the insurance industry is that enrollment numbers are falling short of projections . One insurance company executive put it this way , `` The numbers are n't as bad as the doomsday people would say . But so far , they 're low and they have people worried . ''

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White House has n't released numbers on enrollment , leading many to assume it 's low

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Most of attention has focused on difficulties in signing up online for health care exchanges

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HHS spokeswoman : Administration working aggressively to correct problems for insurers

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Official says enrollment numbers are likely to be released in mid-November